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An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it. Its resistance at room temperature $(27.0 ° C)$ is found to be $75.3 Ω$ . When the toaster is connected to a $230 V$ supply, the current settles, after a few seconds, to a steady value of $2.68 A$ . What is the steady temperature of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved, is $1.70 \times 10^{- 4} {{}^{\circ}C}^{- 1}$ .

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$480 ° C$

$850 ° C$

$830 ° C$

$1060 ° C$

answer is B.

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Detailed Solution

Given, $T_{0} = 27 ° C$ and $R_{0} = 75.3 Ω$

$At temperature T, R_{T} = \frac{V_{T}}{i_{T}}$

$= \frac{230}{268} = 85.82 Ω$

$R_{T} = R_{0} [1 + α (T - T_{0})]$

$(R = \frac{V}{i})$

Using the equation, $R_{T} = R_{0} [1 + α (T - T_{0})]$

We have, $85.82 = 75.3 [1 + (1.70 \times 10^{- 4}) (T - 27)]$

Solving, we get

$T \approx 850 ° C$

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